Our review of mathematics begins with a consideration of the scope of mathematics, and compares mathematics to other areas of knowledge. The question of whether math is real or discovered is considered, and the curious relation of abstract thought and its persistent relevance to the natural world is examined. The structure of mathematical knowledge is explored, using John Kemeny's A Philosopher Looks at Science as our guide. The ways of knowing are detailed, and the podcast concludes with an historic overview of the mathematical quest for certainty. Supplementary material relevant to this podcast may be found on the companion site